Strongly $n$-trivial Links are Boundary Links
نویسندگان
چکیده
منابع مشابه
Positive links are strongly quasipositive
Let S(D) be the surface produced by applying Seifert’s algorithm to the oriented link diagram D. I prove that if D has no negative crossings then S(D) is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a fiber surface plumbed from positive Hopf annuli. This result, combined with the truth of the “local Thom Conjecture”, has various interesting consequences; for instance,...
متن کاملNot All Links Are Concordant to Boundary Links
A link is a smooth, oriented submanifold L = {Kx, . . . , Km} of S which is the ordered disjoint union of m manifolds each piecewise-linearly homeomorphic to the «-sphere (if m = 1, L is called a knot). Knots and links play an essential role in the classification of manifolds and, in this regard, perhaps the most important equivalence relation on links is that of link concordance. LQ and L{ are...
متن کاملA New Proof That Alternating Links Are Non-trivial
We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory. 1. Statement of Results There are several approaches in the literature for showing that alternating links are non-trivial. Most of these approaches rely upon the use of a powerful kno...
متن کاملStrongly n-trivial Knots
We prove that given any knot k of genus g, k fails to be strongly n-trivial for all n, n ≥ 3g − 1.
متن کاملJu l 1 99 8 POSITIVE LINKS ARE STRONGLY
Given an oriented link diagram D, let X>(D) (resp., X<(D)) be the set of positive (resp., negative) crossings, and O≥(D) (resp., O<(D)) the set of Seifert circles adjacent to some x ∈ X>(D) (resp., to no x ∈ X>(D)). Write #A for the number of elements of A. Let S(D) be the surface produced by applying Seifert’s algorithm to D; let L(D) := ∂S(D). An oriented link L is positive if L is isotopic t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2007
ISSN: 0387-3870
DOI: 10.3836/tjm/1202136680